(6x-7)(x-9)=(x-3)(1-5x)

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Solution for (6x-7)(x-9)=(x-3)(1-5x) equation: 


Simplifying
(6x + -7)(x + -9) = (x + -3)(1 + -5x)

Reorder the terms:
(-7 + 6x)(x + -9) = (x + -3)(1 + -5x)

Reorder the terms:
(-7 + 6x)(-9 + x) = (x + -3)(1 + -5x)

Multiply (-7 + 6x) * (-9 + x)
(-7(-9 + x) + 6x * (-9 + x)) = (x + -3)(1 + -5x)
((-9 * -7 + x * -7) + 6x * (-9 + x)) = (x + -3)(1 + -5x)
((63 + -7x) + 6x * (-9 + x)) = (x + -3)(1 + -5x)
(63 + -7x + (-9 * 6x + x * 6x)) = (x + -3)(1 + -5x)
(63 + -7x + (-54x + 6x2)) = (x + -3)(1 + -5x)

Combine like terms: -7x + -54x = -61x
(63 + -61x + 6x2) = (x + -3)(1 + -5x)

Reorder the terms:
63 + -61x + 6x2 = (-3 + x)(1 + -5x)

Multiply (-3 + x) * (1 + -5x)
63 + -61x + 6x2 = (-3(1 + -5x) + x(1 + -5x))
63 + -61x + 6x2 = ((1 * -3 + -5x * -3) + x(1 + -5x))
63 + -61x + 6x2 = ((-3 + 15x) + x(1 + -5x))
63 + -61x + 6x2 = (-3 + 15x + (1 * x + -5x * x))
63 + -61x + 6x2 = (-3 + 15x + (1x + -5x2))

Combine like terms: 15x + 1x = 16x
63 + -61x + 6x2 = (-3 + 16x + -5x2)

Solving
63 + -61x + 6x2 = -3 + 16x + -5x2

Solving for variable 'x'.

Reorder the terms:
63 + 3 + -61x + -16x + 6x2 + 5x2 = -3 + 16x + -5x2 + 3 + -16x + 5x2

Combine like terms: 63 + 3 = 66
66 + -61x + -16x + 6x2 + 5x2 = -3 + 16x + -5x2 + 3 + -16x + 5x2

Combine like terms: -61x + -16x = -77x
66 + -77x + 6x2 + 5x2 = -3 + 16x + -5x2 + 3 + -16x + 5x2

Combine like terms: 6x2 + 5x2 = 11x2
66 + -77x + 11x2 = -3 + 16x + -5x2 + 3 + -16x + 5x2

Reorder the terms:
66 + -77x + 11x2 = -3 + 3 + 16x + -16x + -5x2 + 5x2

Combine like terms: -3 + 3 = 0
66 + -77x + 11x2 = 0 + 16x + -16x + -5x2 + 5x2
66 + -77x + 11x2 = 16x + -16x + -5x2 + 5x2

Combine like terms: 16x + -16x = 0
66 + -77x + 11x2 = 0 + -5x2 + 5x2
66 + -77x + 11x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
66 + -77x + 11x2 = 0

Factor out the Greatest Common Factor (GCF), '11'.
11(6 + -7x + x2) = 0

Factor a trinomial.
11((1 + -1x)(6 + -1x)) = 0

Ignore the factor 11.

Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {1, 6}

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